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            <h2><font color="#ffffff">Search Algorithms: svarFCI</font></h2>
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<p>
    The svarFCI algorithm is a version of FCI for time series data. See the FCI documentation for a

    description of the FCI algorithm, which allows for unmeasured (hidden, latent) variables in the

    data-generating process and produces a PAG (partial ancestral graph).
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<p>
    svarFCI takes as input a <em>time lag data set</em>, i.e., a data set which includes time series observations

    of variables X1, X2, X3, ..., and their lags X1:1, X2:1, X3:1, ..., X1:2, X2:2, X3:2, ... and so on.

    X1:n is the nth-lag of the variable X1. To create a time lag data set from a standard tabular data

    set (i.e., a matrix of observations of X1, X2, X3, ...), use the <em>create time lag data</em> function in

    the data manipulation toolbox. The user will be prompted to specify the number of lags (n), and a

    new data set will be created with the above naming convention. The new sample size will be

    equal to the original sample size minus n.

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<p>

    Just like the FCI algorithm, SvarFCI operates by checking conditional independence facts. So, the

    algorithm can handle continuous or discrete data and Gaussian or non-Gaussian distributions

    according to the independence test selected. Just as with FCI, the user must choose a value for

    the tuning parameter <em>depErrorsAlpha</em> which determines a cut-off threshold for conditional independence

    tests.
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<p>

    The difference between SvarFCI and FCI is that SvarFCI will automatically respect the time order of

    the variables and impose a repeating structure. Firstly, it puts lagged variables in appropriate tiers

    so, e.g., X3:2 can cause X3:1 and X3 but X3:1 cannot cause X3:2 and X3 cannot cause either

    X3:1 or X3:2. Also, it will assume that the causal structure is the same across time, so that if X1

    is independent of X2 given X3:1, then also X1:1 is independent of X2:1 given X3:2, and so on

    for additional lags if they exist. When some edge is removed as the result of a conditional

    independence test, all similar (or <em>homologous</em>) edges are also removed. Note that this

    implementation does not carry out the independence tests for homologous sets of variables, it

    just assumes that the appropriate lagged independencies hold and removes appropriate edges. (If

    X1 is independent of X2 given X3:1, but X1:1 is not independent of X2:1 given X3:3 due to

    finite sample effects at some cut-off threshold, this discrepancy will not be detected by the

    algorithm: the edge between X1:1 and X2:1 would be removed.)
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<p>

    See Enter and Hoyer (2010) for reference. Note that Enter and Hoyer assume no causal

    connections among contemporaneous variables, i.e., variables at the same lag; SvarFCI as

    implemented here does allow for contemporaneous causal connections (unless explicitly

    forbidden by user-provided background knowledge).
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<p>
    References:
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<ol>
    <li>Entner, D., & Hoyer, P. O. (2010). On causal discovery from time series data using FCI.
    <li>Proceedings of the Fifth European Workshop on Probabilistic Graphical Models, 121-128.
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